An underlying asset with price process , where as both a European put and a European call option contract with the same strike price and maturity written on it. At time the price of the call option is given by,

where is the risk neutral probability. Write down the pricing formula for the put option.

Derive the Put-Call parity equation,

Solution...

the price of a European call written on a non-dividend-paying stock is given by...

where and the price of a the corresponding European put is given by

Hence for the put-call parity we get...

= ...?

I need to simplify the part so I can bring it into the parts and make a substitution but I don't know how to go about doing this...